devtools::load_all()
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# Test functions dictionary:
as.data.table(tfun_dict)
#> key label xdim limits_lower limits_upper
#> 1: TF_Gfunction Gfunction NA NA NA
#> 2: TF_GoldsteinPrice GoldsteinPrice 2 0,0 1,1
#> 3: TF_GoldsteinPriceLog GoldsteinPriceLog 2 0,0 1,1
#> 4: TF_OTL_Circuit OTL_Circuit 6 NA NA
#> 5: TF_RoosArnold RoosArnold NA NA NA
#> 6: TF_ackley ackley 2 0,0 1,1
#> 7: TF_banana banana 2 0,0 1,1
#> 8: TF_beale beale 2 0,0 1,1
#> 9: TF_borehole borehole 2 0,0 1.5,1.0
#> 10: TF_branin branin 2 -2,-2 3,3
#> 11: TF_currin1991 currin1991 2 0,0 1,1
#> 12: TF_easom easom 2 0,0 1,1
#> 13: TF_franke franke 2 -0.5,-0.5 1,1
#> 14: TF_gaussian1 gaussian1 NA NA NA
#> 15: TF_griewank griewank NA NA NA
#> 16: TF_hartmann hartmann 6 NA NA
#> 17: TF_hump hump 2 0,0 1,1
#> 18: TF_levy levy NA NA NA
#> 19: TF_lim2002 lim2002 2 0,0 1,1
#> 20: TF_linkletter_nosignal linkletter_nosignal NA NA NA
#> 21: TF_michalewicz michalewicz NA NA NA
#> 22: TF_piston piston 7 NA NA
#> 23: TF_powsin powsin NA NA NA
#> 24: TF_quad_peaks quad_peaks 2 0,0 1,1
#> 25: TF_quad_peaks_slant quad_peaks_slant 2 0,0 1,1
#> 26: TF_rastrigin rastrigin NA NA NA
#> 27: TF_robotarm robotarm 8 NA NA
#> 28: TF_sinumoid sinumoid 2 0,0 1,1
#> 29: TF_sqrtsin sqrtsin NA NA NA
#> 30: TF_waterfall waterfall 2 0,0 1,1
#> 31: TF_wingweight wingweight 10 NA NA
#> 32: TF_zhou1998 zhou1998 2 0,0 1,1
#> key label xdim limits_lower limits_upper
# Get objective to define the "problem":
obj = tfun_dict$get("TF_banana")
# Define optimizers based on the objective and conduct 1000 steps:
oo1 = OptimizerGD$new(obj, x_start = c(0.6, 0.6), step_size = 0.001, id = "GD x0=(0.6, 0.6)", print_trace = FALSE)
oo1$optimize(steps = 1000)
oo2 = OptimizerGD$new(obj, x_start = c(0, 0), step_size = 0.001, id = "GD x0=(0, 0)", print_trace = FALSE)
oo2$optimize(steps = 1000)
oo3 = OptimizerGD$new(obj, x_start = c(0.4, 1), step_size = 0.001, id = "GD x0=(0.4, 1)", print_trace = FALSE)
oo3$optimize(steps = 1000)
oo4 = OptimizerMomentum$new(obj, x_start = c(0, 0), step_size = 0.001, print_trace = FALSE)
oo4$optimize(steps = 1000)
oo5 = OptimizerNAG$new(obj, x_start = c(0, 0), step_size = 0.001, print_trace = FALSE)
oo5$optimize(steps = 1000)
# Optimization traces are stored in the archive:
oo5$archive
#> x_out x_in update fval_out
#> 1: -0.003283, 0.001231 0,0 -0.003283, 0.001231 0.09392
#> 2: -0.008732, 0.003367 -0.003283, 0.001231 -0.005449, 0.002136 0.10979
#> 3: -0.014160, 0.005742 -0.008732, 0.003367 -0.005427, 0.002375 0.11764
#> 4: -0.017796, 0.007793 -0.014160, 0.005742 -0.003637, 0.002051 0.11707
#> 5: -0.019140, 0.009341 -0.017796, 0.007793 -0.001344, 0.001548 0.11544
#> ---
#> 996: 0.5000,0.8667 0.5000,0.8667 1.159e-32,5.911e-33 1.00000
#> 997: 0.5000,0.8667 0.5000,0.8667 1.043e-32,5.320e-33 1.00000
#> 998: 0.5000,0.8667 0.5000,0.8667 9.388e-33,4.788e-33 1.00000
#> 999: 0.5000,0.8667 0.5000,0.8667 8.449e-33,4.309e-33 1.00000
#> 1000: 0.5000,0.8667 0.5000,0.8667 7.604e-33,3.878e-33 1.00000
#> fval_in lr objective momentum step batch
#> 1: 0.08208 0.001 <Objective[17]> 0.9 1 1
#> 2: 0.09392 0.001 <Objective[17]> 0.9 2 1
#> 3: 0.10979 0.001 <Objective[17]> 0.9 3 1
#> 4: 0.11764 0.001 <Objective[17]> 0.9 4 1
#> 5: 0.11707 0.001 <Objective[17]> 0.9 5 1
#> ---
#> 996: 1.00000 0.001 <Objective[17]> 0.9 996 1
#> 997: 1.00000 0.001 <Objective[17]> 0.9 997 1
#> 998: 1.00000 0.001 <Objective[17]> 0.9 998 1
#> 999: 1.00000 0.001 <Objective[17]> 0.9 999 1
#> 1000: 1.00000 0.001 <Objective[17]> 0.9 1000 1
# The Visualizer class just requires the object and sets everything such as
# limits automatically (if not you will get a message):
viz = Visualizer$new(obj)
# The two potential visualizations are surface and contour plots. The "base"
# layer is defined by `$initLayerContour()` or `$initLayerSurface()`:
viz$initLayerSurface()# Creating the figure is done with `$plot()`:
viz$plot()
# To quickly add the optimization traces use `$addLayerOptimizationTrace(opt)`:
viz$addLayerOptimizationTrace(oo1) # The color is randomly generated if not defined
viz$addLayerOptimizationTrace(oo2, line_color = "rgb(46,139,87)")
viz$addLayerOptimizationTrace(oo3, line_color = "rgb(220,20,60)")
viz$addLayerOptimizationTrace(oo4)
viz$addLayerOptimizationTrace(oo5)viz$plot()
# If traces overlap, we can add an offset to slightly shift them:
viz$initLayerSurface()
viz$addLayerOptimizationTrace(oo1)
viz$addLayerOptimizationTrace(oo2, line_color = "rgb(46,139,87)", offset = c(-0.01, -0.01, -0.01))
viz$addLayerOptimizationTrace(oo3, line_color = "rgb(220,20,60)")
viz$addLayerOptimizationTrace(oo4, offset = c(0.01, 0.01, -0.01))
viz$addLayerOptimizationTrace(oo5, offset = c(0.01, 0.01, 0.01))viz$plot()
# Setting the scene and layout can be done with `$setScene()` and `setLayout()`:
viz$setScene(1, -2, 1)
viz$setLayout(legend = list(
orientation = "h", # show entries horizontally
xanchor = "center", # use center of legend as anchor
x = 0.5)) # legend = list()viz$plot()
# Save a plot can also easily be done with `save()`
viz$save("myfigure.png")
# Create animations with `$animate()` (Note: Just the frames are stored,
# you have to put them together by yourself):
viz$animate(nframes = 24L, view_start = list(x = 1, y = -2, z = 1),
view_end = list(x = 0.5, y = -2, z = 1))
# Use, e.g., ImageMagick: `convert -delay 20 -loop 0 animation/*.png mygif.gif`
# Define the linear model loss function:
mylm = function(x, Xmat, y) {
l2norm(Xmat %*% x - y)
}
# Use the iris dataset with response `Sepal.Width` and feature `Petal.Width`:
Xmat = model.matrix(~ Petal.Width, data = iris)
y = iris$Sepal.Width
# Create a new object:
obj_lm = Objective$new(id = "iris LM", fun = mylm, xdim = 2, Xmat = Xmat, y = y, minimize = TRUE)
# Optimize with two different start points:
oo1 = OptimizerGD$new(obj_lm, x_start = c(0, -0.05), step_size = 0.001, print_trace = FALSE)
oo1$optimize(steps = 100)
tail(oo1$archive)
#> x_out x_in update fval_out fval_in lr
#> 1: 1.0466,0.9257 1.0381,0.9216 0.008494,0.004121 16.05 16.14 0.001
#> 2: 1.0550,0.9296 1.0466,0.9257 0.008415,0.003971 15.97 16.05 0.001
#> 3: 1.0633,0.9335 1.0550,0.9296 0.008336,0.003823 15.88 15.97 0.001
#> 4: 1.0716,0.9371 1.0633,0.9335 0.008258,0.003676 15.80 15.88 0.001
#> 5: 1.0798,0.9407 1.0716,0.9371 0.00818,0.00353 15.72 15.80 0.001
#> 6: 1.0879,0.9441 1.0798,0.9407 0.008103,0.003386 15.65 15.72 0.001
#> objective momentum step batch
#> 1: <Objective[17]> 0 95 1
#> 2: <Objective[17]> 0 96 1
#> 3: <Objective[17]> 0 97 1
#> 4: <Objective[17]> 0 98 1
#> 5: <Objective[17]> 0 99 1
#> 6: <Objective[17]> 0 100 1
oo2 = OptimizerMomentum$new(obj_lm, x_start = c(-0.05, 0), step_size = 0.001, print_trace = FALSE)
oo2$optimize(steps = 100)
tail(oo2$archive)
#> x_out x_in update fval_out fval_in
#> 1: 3.3463,-0.2398 3.3417,-0.2393 0.004586,-0.000567 4.959 4.959
#> 2: 3.3504,-0.2399 3.3463,-0.2398 0.00408801,-0.00002542 4.960 4.959
#> 3: 3.3539,-0.2396 3.3504,-0.2399 0.0035171,0.0003152 4.960 4.960
#> 4: 3.3568,-0.2391 3.3539,-0.2396 0.002885,0.000475 4.961 4.960
#> 5: 3.3590,-0.2386 3.3568,-0.2391 0.0022125,0.0004852 4.962 4.961
#> 6: 3.3605,-0.2382 3.3590,-0.2386 0.0015226,0.0003845 4.963 4.962
#> lr objective momentum step batch
#> 1: 0.001 <Objective[17]> 0.9 95 1
#> 2: 0.001 <Objective[17]> 0.9 96 1
#> 3: 0.001 <Objective[17]> 0.9 97 1
#> 4: 0.001 <Objective[17]> 0.9 98 1
#> 5: 0.001 <Objective[17]> 0.9 99 1
#> 6: 0.001 <Objective[17]> 0.9 100 1
oo3 = OptimizerNAG$new(obj_lm, x_start = c(0, 0), step_size = 0.001, print_trace = FALSE)
oo3$optimize(steps = 100)
tail(oo3$archive)
#> x_out x_in update fval_out fval_in lr
#> 1: 3.3395,-0.2304 3.3366,-0.2287 0.002835,-0.001660 4.955 4.955 0.001
#> 2: 3.3418,-0.2317 3.3395,-0.2304 0.002351,-0.001342 4.956 4.955 0.001
#> 3: 3.3437,-0.2328 3.3418,-0.2317 0.001895,-0.001061 4.957 4.956 0.001
#> 4: 3.3452,-0.2336 3.3437,-0.2328 0.0014699,-0.0008125 4.957 4.957 0.001
#> 5: 3.3463,-0.2342 3.3452,-0.2336 0.0010754,-0.0005926 4.957 4.957 0.001
#> 6: 3.3470,-0.2346 3.3463,-0.2342 0.0007129,-0.0003968 4.958 4.957 0.001
#> objective momentum step batch
#> 1: <Objective[17]> 0.9 95 1
#> 2: <Objective[17]> 0.9 96 1
#> 3: <Objective[17]> 0.9 97 1
#> 4: <Objective[17]> 0.9 98 1
#> 5: <Objective[17]> 0.9 99 1
#> 6: <Objective[17]> 0.9 100 1
# Visualize, this time with contour lines and custom limits:
viz = Visualizer$new(obj_lm, x1limits = c(-0.5, 5), x2limits = c(-3.2, 2.8))
viz$initLayerContour()
viz$addLayerOptimizationTrace(oo1, add_marker_at = round(seq(1, 100, len = 10L)))
viz$addLayerOptimizationTrace(oo2, add_marker_at = c(1, 50, 90), marker_shape = c("square", "star-triangle-down", "cross"))
viz$addLayerOptimizationTrace(oo3, add_marker_at = 100, marker_shape = "star")
viz$setLayout(legend = list(orientation = "h", xanchor = "center", x = 0.5))viz$plot()
viz$animate(nframes = 24L)
# Use, e.g., ImageMagick: `convert -delay 10 -loop 0 animation/*.png mygif.gif`
